What are Haar Pyramids?

Question

I'm trying to reproduce (part of) the work in this paper: http://www.mit.edu/~kimo/publications/harmonization/

I can't figure out quite what they mean by "Haar pyramids". I've found all kinds of things on the Gaussian and Laplacian image pyramids, as well as plenty on Haar filters, but nowhere (outside of this paper) have I found anything that is referred to as a "Haar pyramid".

At the moment, I'm using roughly the 2D Haar transform linked to at the bottom of this page (slightly edited to work with my own image format): http://www.cs.ucf.edu/~mali/haar/

When given this:

It produces this:

Is this what I'm looking for? I'm having trouble understanding how there is any advantage to processing images in this format. Also, the paper mentions that they use "oversampled" Haar pyramids, which I believe means that they aren't resizing the image on each pass through the filter. If that's the case, then how can I store all of these images compactly? I like the code I have because it stores everything in just one bitmap, and the thought of having to store an array of multiple instances of the picture is not too attractive.

The slightest insight into any part of my question would be much appreciated. Thanks!

Answer 1

Haar pyramid is like Gaussian pyramid but with Haar filter at each level.

• oversampled in this case I understand it means exactly this, no resizing (downsampling).
• i suspect that no compact representation exist. There is reference in the paper that I haven't read but can give more information on the subject paper

"... and the thought of having to store an array of multiple instances of the picture is not too attractive" - This type of image manipulation is expected to be heavy on resources and processing, so holding multiple instances of processed images is not unusual.